It should indeed, and in hindsight it would have been better to move int to 64 bits (especially for C's integer promotion, which only really makes sense when the promotion happens to the register width.
But porting 32-bit code to 64-bit was a big deal back then, and C99 with its new fixed-width integer types overlapped with the first AMD64 CPUs (and Microsoft's MSVC didn't start to support C99 until around 2015 anyway), I guess keeping int on 32-bits in the popular compilers was deemed 'safer' for porting existing code. I guess we can already be lucky that all the big compilers agreed on the same int width.
But porting 32-bit code to 64-bit was a big deal back then, and C99 with its new fixed-width integer types overlapped with the first AMD64 CPUs (and Microsoft's MSVC didn't start to support C99 until around 2015 anyway), I guess keeping int on 32-bits in the popular compilers was deemed 'safer' for porting existing code. I guess we can already be lucky that all the big compilers agreed on the same int width.